As is described in Patent Document 1, a multi-plate-stack-type heat exchanger is used in automotive oil coolers. The heat exchanger of such type comprises a plurality of core plates that have, around peripheral edges of respective base portions thereof, outer peripheral tapered portions extending toward an outer peripheral side and are stacked on one another, and the outer peripheral tapered portions of adjacent core plates are joined to each other by brazing, so that a heat exchanging fluid passage is formed between the base portions of the adjacent core plates.